Reduced Drag System for Windmills, Fans, Propellers, Airfoils and Hydrofoils

ABSTRACT

Airfoil and hydrofoils systems with structures having a surface texture defined by fractal geometries are described. Raised portions or fractal bumps can be included on the surfaces, forming a surface texture. The surface textures can be defined by two-dimensional fractal shapes, partial two-dimensional fractal shapes, non-contiguous fractal shapes, three-dimensional fractal objects, and partial three-dimensional fractal objects. The surfaces can include indents having fractal geometries. The indents can have varying depths and can be bordered by other indents, or bumps, or smooth portions of the airfoil or hydrofoil structure. The fractal surface textures can reduce vortices inherent from airfoil and hydrofoil structures. The roughness and distribution of the fractal surface textures reduce the vortices, improving laminar flow characteristics and at the same time reducing drag. The systems are passive and do not require applied power.

RELATED APPLICATION

This application is a division of U.S. patent application Ser. No.12/606,764 entitled “Reduced Drag System for Windmills, Fans,Propellers, Airfoils and Hydrofoils,” filed Oct. 27, 2009, which claimsthe benefit of U.S. Provisional Patent Application No. 61/198,037,entitled “Reduced Drag System for Windmills, Fans, Propellers, andAirfoils,” filed 1 Nov. 2008, the entire contents of which areincorporated herein by reference.

BACKGROUND

There are numerous prior art airfoil and hydrofoil structures, such as acommon commercial airplane wing. The surface textures of such structuresare typically smooth or include small surface protrusions such as poprivets and the like. All of such surfaces are typically defined byEuclidean geometry and produce well-known turbulence effects.

Many fluid dynamics phenomena, such as aerodynamic turbulence, however,do not possess Euclidean geometric characteristics. They can, on theother hand, be analyzed using fractal geometry. Fractal geometrycomprises an alternative set of geometric principles conceived anddeveloped by Benoit B. Mandelbrot. An important treatise on the study offractal geometry is Mandelbrot's The Fractal Geometry of Nature.

As discussed in Mandelbrot's treatise, many forms in nature are soirregular and fragmented that Euclidean geometry is not adequate torepresent them. In his treatise, Mandelbrot identified a family ofshapes, which described the irregular and fragmented shapes in nature,and called them fractals. A fractal is defined by its topologicaldimension D_(T) and its Hausdorf dimension D. As defined, D_(T) isalways an integer, D need not be an integer, and D≧D_(T). (See p. 15 ofMandelbrot's The Fractal Geometry of Nature). Fractals may berepresented by two-dimensional shapes and three-dimensional objects. Inaddition, fractals possess self-similarity in that they have the sameshapes or structures on both small and large scales.

It has been found that fractals have characteristics that aresignificant in a variety of fields. For example, fractals correspondwith naturally occurring phenomena such as aerodynamic phenomena. Inaddition, three-dimensional fractals have very specific electromagneticwave-propagation properties that lead to special wave-matter interactionmodes. Fractal geometry is also useful in describing naturally occurringforms and objects such as a stretch of coastline. Although the distanceof the stretch may be measured along a straight line between two pointson the coastline, the distance may be more accurately consideredinfinite as one considers in detail the irregular twists and turns ofthe coastline.

Fractals can be generated based on their property of self-similarity bymeans of a recursive algorithm. In addition, fractals can be generatedby various initiators and generators as illustrated in Mandelbrot'streatise.

An example of a three-dimensional fractal is illustrated in U.S. Pat.No. 5,355,318 to Dionnet et al., the entire contents of which areincorporated herein by reference. The three-dimensional fractaldescribed in this patent is referred to as Serpienski's mesh. This meshis created by performing repeated scaling reductions of a parenttriangle into daughter triangles until the daughter triangles becomeinfinitely small. The dimension of the fractal is given by therelationship (log N)/(log E) where N is the number of daughter trianglesin the fractal and E is a scale factor.

Some processes for making self-similar three-dimensional fractals isknown. For example, the Dionnet et al. patent discloses methods ofenabling three-dimensional fractals to be manufactured. The methodconsists in performing repeated scaling reductions on a parent generatordefined by means of three-dimensional coordinates, in storing thecoordinates of each daughter object obtained by such a scalingreduction, and in repeating the scaling reduction until the dimensionsof a daughter object become less than a given threshold value. Thecoordinates of the daughter objects are then supplied to astereolithographic apparatus which manufactures the fractal defined byassembling together the daughter objects.

In addition, U.S. Pat. No. 5,132,831 to Shih et al. discloses an analogoptical processor for performing affine transformations and constructingthree-dimensional fractals that may be used to model natural objectssuch as trees and mountains. An affine transformation is a mathematicaltransformation equivalent to a rotation, translation, and contraction(or expansion) with respect to a fixed origin and coordinate system.There are also a number of prior-art patents directed towardtwo-dimensional fractal image generation. For example, European PatentNo. 0 463 766 A2 to Applicant GEC-Marconi Ltd. discloses a method ofgenerating fractal images representing fractal objects. This inventionis particularly applicable to the generation of terrain images. Inaddition, U.S. Pat. No. 4,694,407 to Ogden discloses fractal generation,as for video graphic displays. Two-dimensional fractal images aregenerated by convolving a basic shape, or “generator pattern,” with a“seed pattern” of dots, in each of different spatial scalings.

Fractal patterns have be used for radio receivers and transceivers, asdescribed in U.S. Pat. No. 6,452,553 to Cohen, and U.S. Pat. No.7,126,537 to Cohen, the entire contents of both of which areincorporated herein by reference. See also Hohlfeld, R., and Cohen, N.,“SELF-SIMILARITY AND THE GEOMETRIC REQUIREMENTS FOR FREQUENCYINDEPENDENCE IN ANTENNAE,” Fractals, Vol. 7, No. 1 (1999) 79-84, theentire contents of which are incorporated herein by reference.

Thus, as current techniques for shaping airfoils, hydrofoils, and otherfluid-contact surfaces are based on Euclidean geometries, such surfacescreate undesirable turbulences effects, including reduced fuelefficiency and reduced maneuverability. Additional undesirableturbulence effects can include the potentially deleterious eddy currentsor vortexes produced by large scale commercial aircraft, which can poseproblems or hazards for other aircraft including smaller commercial andprivate aircraft. Consequently, there a need exists to improve surfacesof airfoils and hydrofoils for reduced drag and improved manuererabilitycharacteristics.

SUMMARY

Aspects and embodiments of the present disclosure address theshortcomings noted previously by implementing or providing fractalshaped surface features to airfoils and hydrofoils, as well as otherfluid-contact surfaces.

Embodiments, of the present disclosure are directed to airfoil andhydrofoils systems with structures having a surface texture defined byfractal geometries. Raised portions or fractal bumps can be included onthe surfaces, forming a surface texture. The surface textures can bedefined by two-dimensional fractal shapes, partial two-dimensionalfractal shapes, non-contiguous fractal shapes, three-dimensional fractalobjects, and partial three-dimensional fractal objects. The surfaces caninclude indents or depressions having fractal geometries. The indentscan have varying depths and can be bordered by other indents, or bumps,or smooth portions of the airfoil or hydrofoil structure. The fractalsurface textures can reduce vortices inherent from airfoil and hydrofoilstructures. The roughness and distribution of the fractal surfacetextures reduce the vortices, improving laminar flow characteristics andat the same time reducing drag. The systems are passive and do notrequire applied power.

In exemplary embodiments, the distribution of the fractal featuresthemselves can also have a fractal nature, such as conforming to alogarithmic distribution in one or more directions along the airfoil orhydrofoil. Some embodiments can include small holes or pin holes havingsuch a distribution. Fluid such as air or water can be caused to flowfrom such holes to reduce turbulence, in some applications.

Other features and advantages of the present disclosure will beunderstood upon reading and understanding the detailed description ofexemplary embodiments, described herein, in conjunction with referenceto the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of the present disclosure may be more fully understood from thefollowing description when read together with the accompanying drawings,which are to be regarded as illustrative in nature, and not as limiting.The drawings are not necessarily to scale, emphasis instead being placedon the principles of the disclosure. In the drawings:

FIG. 1A depicts a perspective view of a representative airfoil havingfractal surface features, in accordance with an exemplary embodiment ofthe present disclosure;

FIG. 1B depicts a top view of a fractal surface, based on a Koch star,for fluid-contact surfaces, in accordance with exemplary embodiments ofthe present disclosure;

FIG. 1C depicts a top view of a fractal surface, based on a Quadric Kochisland, for fluid-contact surfaces, in accordance with exemplaryembodiments of the present disclosure;

FIG. 1D depicts a surface feature having a fractal shape in the form ofa generic affine de Rham curve;

FIG. 2 depicts an airplane with surfaces having fractal textures, inaccordance with exemplary embodiments of the present disclosure.

FIG. 3 depicts a cross sectional view of the boundary layer air flowaround a prior art streamlined body representing an airship with a viewof the detached flows and turbulent wake;

FIG. 4 depicts a cross sectional view of the boundary layer air flowaround a streamlined body representing an airship with a view of thelaminar flow, in accordance with an embodiment of the presentdisclosure;

FIG. 5 depicts a partial perspective view of a stern portion of a hullof a submerged water vessel having hydrofoil planes and rudders withfractal surface features, in accordance with exemplary embodiments ofthe present disclosure;

FIG. 6 depicts a fluid-contact surface with a number of turbulencereducing surface features, in accordance with an embodiment of thepresent disclosure; and

FIG. 7 depicts an alternate fluid-contact surface with a number ofturbulence reducing surface features, in accordance with an embodimentof the present disclosure.

While certain embodiments are depicted in the drawings, one skilled inthe art will appreciate that the embodiments depicted are illustrativeand that variations of those shown, as well as other embodimentsdescribed herein, may be envisioned and practiced within the scope ofthe present disclosure.

DETAILED DESCRIPTION

As described previously, embodiments of the present disclosure aredirected to airfoils and hydrofoils, and systems using the same, inwhich fluid-contacting structures (e.g., wings, fins, etc.) have asurface texture defined by fractal geometries. By inclusion of thefractal-based textures or shapes, reduced drag and increasedmaneuverability can be provided.

Raised portions or fractal bumps can be included on the surfaces,forming a surface texture. The surface textures can be defined bytwo-dimensional fractal shapes, partial two-dimensional fractal shapes,non-contiguous fractal shapes, three-dimensional fractal objects, andpartial three-dimensional fractal objects. The surfaces can includeindents or depressions having fractal geometries. The indents can havevarying depths and can be bordered by other indents, or bumps, or smoothportions of the airfoil or hydrofoil structure. The fractal surfacetextures can reduce vortices inherent from airfoil and hydrofoilstructures. The roughness and distribution of the fractal surfacetextures reduce the vortices, improving laminar flow characteristics andat the same time reducing drag. The systems are passive and do notrequire applied power.

The distribution of the fractal features itself can also have a fractalnature, such as conforming to a logarithmic distribution in one or moredirections along the airfoil or hydrofoil. Some embodiments can includesmall holes or pin holes having such a distribution. In exemplaryembodiments, the small holes can allow forced gas or liquid to flow outof the airfoil or hydrofoil surface to further minimize deleteriousturbulence effects. Water or compressed gas (air) can be used, forexample, as described in U.S. Pat. No. 7,290,738, the entire contents ofwhich are incorporated herein by reference.

Fractal shapes described herein can be fabricated or made for hydrofoiland airfoil surfaces by computer-aided design, computer-aidedmanufacturing (“CAD” or “CAM”) techniques. Suitable techniques aredescribed in U.S. Pat. No. 5,355,318 to Dionnet et al., which isincorporated herein by reference in its entirety. Plates or surfaceshaving 3D fractal shapes can be affixed to or incorporated in a portionof an airfoil or hydrofoil.

FIG. 1A depicts a perspective view of a representative fluid-contactsurface, e.g., an airfoil or hydrofoil, having fractal-based surfacefeatures 102A, in accordance with an exemplary embodiment of the presentdisclosure. Surface fractal features 102A can be indentations (or,indents) or protrusions or mixtures of the two. In the figure, twofractal surface features are shown as being 3rd and 4th iteration Kochstars. Of course, other fractal shapes can be used. The surface featurescan function with the fluid-contact surface as a turbulence reductionsystem. In exemplary embodiments closed, or semi-closed fractals can beutilized for an outline of a fractal texture or surface according to thepresent disclosure. Non-closed surface features, e.g., a fern shape orother dendritic shapes, can be used for some applications. As isdescribed in further detail below, such fractal-based surface featurescan include holes or apertures distributed on a fluid contact surface ina “fractal” distribution such as a logarithmic progression. Thefractal-based surface features can be formed directly into or on theunderlying fluid-contact surface or can be made in or formed on anothersurface that is attached to a fluid-contact surface.

Suitable fractal patterns are described in U.S. Pat. No. 6,452,553 toCohen, and U.S. Pat. No. 7,126,537 to Cohen, the entire contents of bothof which are incorporated herein by reference. See also Hohlfeld, R.,and Cohen, N., “SELF-SIMILARITY AND THE GEOMETRIC REQUIREMENTS FORFREQUENCY INDEPENDENCE IN ANTENNAE,” Fractals, Vol. 7, No. 1 (1999)79-84, the entire contents of which are incorporated herein byreference.

FIG. 1B depicts a top view of a fractal-textured fluid contact surface102B, based on a Koch star, for fluid-contact surfaces, in accordancewith exemplary embodiments of the present disclosure. Surface 102Bincludes multiple units 104B, each having a fractal shape 106B. Eachfractal shape 106B can have a desired topographic profile (or profilenormal to the surrounding fluid contact surface), e.g., wing or fin.

FIG. 1C depicts a top view of a fractal containing fluid-contact surface102C, based on a Quadric Koch island, for fluid-contact surfaces, inaccordance with exemplary embodiments of the present disclosure. Unitsor cells 104C are shown containing individual fractal textures(depressions or protrusions) 106C. Other fractal shapes can of course beused according to the present disclose. FIG. 1D shows another fractalshape.

FIG. 1D depicts a surface feature 102D having a fractal shape in theform of a generic affine de Rham curve. The curve in the figure is forα=0.5,β=1.0,δ=0.33,ε=−0.38,ζ=−0.18,η=−0.42. Fractal surfaces can haveprotrusions or depression having a general outline as shown in FIG. 1D,with peaks or troughs that result in pyramidal shapes. Any suitable typeof de Rham curve may be used, and not only the curve shown in thedrawing. See, Georges de Rham, On Some Curves Defined by FunctionalEquations (1957), reprinted in Classics on Fractals, ed. Gerald A. Edgar(Addison-Wesley, 1993), pp. 285-298, the entire contents of which areincorporated herein by reference.

Of course, while FIGS. 1B-1C show detail of fractal surfaces having amore or less uniform distribution or surface density of fractal features(e.g., 104B in FIG. 1B), the surface density (2D distribution) or lineardistribution in any surface direction can vary. In exemplaryembodiments, the distribution of surface features can be other thanuniform. For example, surface features (such as holes or fractal-shapedfeatures) can have a logarithmic distribution along an airfoil orhydrofoil surface.

FIG. 2 depicts an airplane 200 with surfaces having fractal textures, inaccordance with exemplary embodiments of the present disclosure. Plane200 has a fuselage 201, with a midline 202, and wings 210. A number ofpassenger seats 203 and typical direction of flight 1, are shown forease in comprehension. The surface of the airplane 200 can have a numberof surface features 216(1-N) for reducing turbulence effects. Thesurface features 216(1-N) can be located at desired locations on theairplane 200. Wing locations 220, tail locations 222, and enginelocations 224 are shown as examples. The surface features 216(1-N) ateach location can be configured in desired ways. Examples include butare not limited to parallel rows with regular spacings, in rectangulararrays, in offset parallel rows, or rows with spacings that arenon-uniform. As an example of the latter, wing location 220 depicts rowsA-C conforming to a logarithmic (linear density) distribution along thedirection of flight 1.

FIG. 3 depicts a cross sectional view 300 of the boundary layer air flowaround a prior art streamlined body representing an airship 302 with aview of the detached flows and turbulent wake. The detached air flow 343and the turbulent wake 346 resulting in drag are shown. Also shown arethe onset 345 of the turbulent boundary layer flow and the turbulentboundary layer flow 344 itself all of which contribute to drag on thebody. The boundary layer thickness normally increases monotonically as adistance from the foremost portion of the airship along its body 341. Atthe nose the boundary layer thickness is negligible. As long as theairship body is sufficiently smooth and devoid of a strong temperaturegradient, the boundary layer flow 342 is typically laminar in thefavorable pressure gradient region of the fore section of the airshipwhere the cross-section is rapidly expanding. The boundary layerthickness thickens slowly and usually does not exceed a few centimetersbefore the onset 345 of boundary layer turbulence. In the neutral andadverse pressure region along the body, however, the growth of theboundary layer quickens and inevitably becomes less stable andultimately develops into an unstable flow pattern, marking the onset ofturbulent flow 344. The process in known as boundary layer transition.The transition can occur in the neutral region as well as the adversepressure gradient region as the pressure begins to recover over the aftsection of the body. Boundary layer thickens rapidly after thetransition and normally separates from body near the tail region.

With continued reference to FIG. 3, the effect of the boundary layer onthe drag can be seen as follows, first, the boundary layer adds to thethickness of the body in the form of displacement thickness, whichincreases the pressure drag, and the shear stress at the surface of theairship body 341 creates skin friction drag. The pressure drag isfurther enhanced by the lack of closure of the boundary layer,especially after the detachment of the flow, which prevents the surfacepressure to fully recover. It can be desirable to postpone or eliminatethe transition to turbulence in order to minimize the pressure dragwhich is typically at least an order of magnitude larger than the skinfriction drag. At low Reynolds numbers, which would correspond to an airspeed of well under 1 m/s, it is relatively easy to maintain laminarflow. However, at normal air speed, laminar flow can only be dealt withthrough various prior art boundary layer modification techniques asheretofore discussed such as boundary layer suction, boundary layerblowing or changing the shape of the skin of the airship. The majorityof such techniques are impractical owing to mechanical complexities andincreased weight. A laminar boundary layer also has a stronger tendencyto separate from the body in the strongly adverse pressure regionbecause of the lack of sufficient forward momentum of the laminarboundary layer flow hinders its ability to overcome the negativegradient. Such a separation results in a drastic increase in thepressure drag owing to the large jump in the effective boundary layerthickness as well as the flattening of the pressure recovery. In orderto delay flow detachment, it is often advantageous to deliberately tripthe boundary layer into turbulence even at the expense of increasing theskin friction drag. The richer flow profile of the turbulent boundarylayer enables it to resist the adverse pressure gradient much moreeffectively.

FIG. 4 depicts a cross sectional view 400 of the boundary layer air flowaround a streamlined body 441 representing an airship 402 having surfacefeatures according to the present disclosure, as well as detail oflaminar flow about body 441. Boundary layer air flow 442 is indicatedaround a streamlined body 402 having surface features 416(1-N). It isseen that a nearly constant boundary layer thickness can be maintainedthroughout the adverse gradient region in the aft section of theairship. This efficiency in maintaining the constant boundary layerthickness can be afforded by the presence of surface features 416(1-N).Body 441 is shown as generally a closed ogive shape, which because ofsymmetry can correspond to a top view of a vessel. For otherapplications, phantom line 403 indicates a shape indicative of a crosssection of a wing or fin.

In exemplary embodiments, surface features 416(1-N) are fractal-shapeddepressions or protrusions. Examples can include Koch stars, e.g., asshown in FIG. 1B, in the form of surface depressions or indents of about5 mm to about 30 mm along a major axis and about 5 mm to about 30 mm indepth (or conversely, height); other dimensions can of course be usedand can be varied for water applications.

Of course, while an airship body, is referenced for the description ofFIG. 4, application can be made to portions of an airship body, e.g.,wing, engine, propeller, etc., or to a seagoing vessel as well. Examplesof the latter can include the hull of a boat or body, a propeller blade,or hydrofoils of a submersible vessel.

FIG. 5 depicts a partial perspective view 500 of a stern portion 502 ofa hull 500 of a submerged water vessel having hydrofoil planes 512 andrudders 514 with fractal surface features 516(1-N), in accordance withexemplary embodiments of the present disclosure. Surface features516(1-N) can be fractal-based surface textures, depressions, and/orprotrusions, e.g., based on a Koch star as shown in FIG. 1B. Surfacefeatures 516(1-N) can alternatively be simple holes that have a“fractal” distribution, e.g., logarithmic linear density in one or moreparticular directions. As shown, surface features 516(1-N) may also bepresent on the body of the hull itself.

FIG. 6 depicts a fluid-contact surface 602 with a number of turbulencereducing surface features 616(1-N), in accordance with an embodiment 600of the present disclosure. As shown, the surface features can have anon-uniform distribution on fluid-contact surface 602, e.g., wing. Sucha configuration may be particularly suited for reducing or mitigatingturbulence effects at the junction of a wing and an airplane fuselage,as shown. A direction of wind flow 1 is shown for clarity. In exemplaryembodiments, surface features 616(1-N) can be fractal-based surfacetextures, depressions, and/or protrusions, e.g., based on a Quadric Kochisland as shown in FIG. 1C. Surface features 616(1-N) can alternativelybe simple holes that have a “fractal” distribution, e.g., logarithmiclinear density in one or more particular directions. In exemplaryembodiments, the small holes can allow forced gas or liquid to flow outof the airfoil or hydrofoil surface to further minimize deleteriousturbulence effects. Water or compressed gas (air) can be used, forexample, as described in U.S. Pat. No. 7,290,738, the entire contents ofwhich are incorporated herein by reference.

FIG. 7 depicts an alternate fluid-contact surface with a number ofturbulence reducing surface features, in accordance with an embodiment700 of the present disclosure. As shown, a fluid-contact surface 702 caninclude a number of turbulence reducing surface features 716(1-N), inaccordance with an embodiment 600 of the present disclosure. As shown bycolumns (or rows, depending on perspective) (A)-(E), the surfacefeatures 716(1-N) can have a non-uniform distribution on fluid-contactsurface 702, e.g., wing. As indicated, the distance between successivecolumns can increase (or decrease) according to a logarithmicprogression. In exemplary embodiments, the surface features can bedisposed at a particular area of a hydrofoil or air foil, e.g., atrailing edge, or a leading edge.

Accordingly, embodiments of the present disclosure can reduce ormitigate deleterious turbulence effects for airfoils and hydrofoils byproviding fluid-contacting surfaces with surface features being definedby or distributed according to fractal geometries.

One skilled in the art will appreciate that embodiments of the presentdisclosure, including control algorithms/software/signals for designingor manufacturing fractal shaped surface features, can be implemented inhardware, software, firmware, or any combinations of such, and sent assignals over one or more communications networks such as the Internet.

While certain embodiments have been described herein, it will beunderstood by one skilled in the art that the methods, systems, andapparatus of the present disclosure may be embodied in other specificforms without departing from the spirit thereof.

Accordingly, the embodiments described herein, and as claimed in theattached claims, are to be considered in all respects as illustrative ofthe present disclosure and not restrictive.

What is claimed is:
 1. A drag reduction system comprising: an airfoil ora hydrofoil with a body having a fluid-contact surface operative formovement within a first fluid, wherein the body has a longitudinal axisand, is asymmetrical in cross-section about the longitudinal axis; and aplurality of fractal-based surface features disposed on a portion of thebody and operative to reduce drag when the fluid-contact surface ismoving relative to the first fluid, wherein each of the fractal-basedsurface features comprises (i) an indent on the body, (ii) a fractalshape, and (iii) a hole operative to flow a second fluid from the bodyand into the first fluid to reduce turbulence.
 2. The system of claim 1,wherein the plurality of fractal-based surface features comprise one ormore Koch stars.
 3. The system of claim 1, wherein the plurality offractal-based surface features comprise one or more Quadric Kochislands.
 4. The system of claim 1, wherein the plurality offractal-based surface features comprise indents.
 5. The system of claim1, wherein the one or more fractal-based surface features compriseprotrusions.
 6. The system of claim 5, wherein the one or morefractal-based surface features further comprise indents.
 7. The systemof claim 1, wherein the plurality of fractal-based surface featurescomprise a feature defined by a de Rham curve.
 8. The system of claim 2,wherein the plurality of fractal-based surface features are about 5 mmto about 30 mm along a major axis.
 9. The system of claim 2, wherein theplurality of fractal-based surface features are about 5 mm to about 30mm in depth.
 10. The system of claim 2, wherein the one or morefractal-based surface features are about 5 mm to about 30 mm in height.11. The system of claim 2, wherein the Koch star is a 3rd or 4thiteration Koch star.
 12. The system of claim 1, wherein the plurality offractal-based surface features comprise a plurality of surface featuresconfigured and arranged as an array having multiple rows.
 13. The systemof claim 12, wherein rows of the array are spaced apart in a nonlinearprogression.
 14. The system of claim 13, wherein the nonlinearprogression is parallel to a direction of flight of the fluid-contactsurface.
 15. The system of claim 13, wherein the nonlinear progressionis anti-parallel to a direction of flight of the fluid-contact surface.16. The system of claim 1, wherein the one or more fractal-based surfacefeatures comprise holes in the fluid-contact surface.
 17. The system ofclaim 16, further comprising an air supply for pumping air through theholes to reduce turbulence.
 18. The system of claim 16, furthercomprising an liquid supply for pumping liquid through the holes toreduce turbulence.
 20. The system of claim 1, wherein the plurality offractal-based surface features are disposed on a trailing edge of awing.